Closure of Gunsan facility, one of four GM plants in South Korea, is part of a broader restructuring

General Motors Co. is sending a tough message to thousands of South Korean workers during the Winter Olympics in Pyeongchang, saying it will close a Korean factory in May and pressure union officials for additional cost cuts to stem losses.

The move, announced early Tuesday by GM Korea, is the latest step in a broad global downsizing implemented by Chief Executive Mary Barra, who has closed, shrunk or sold unprofitable business units in India, Russia, Western Europe and Southeast Asia. The largest U.S. auto maker is becoming...